A network representation using nodes interconnected by arcs, provides a powerful visual and conceptual aid for portraying relationships between components of systems. Examples of such systems include an arithmetic expression where operators and operands are connected to each other, a railway system where stations are connected to each other, a telephone system where telephones and exchanges are connected to each other, an organisation where employees and activities are connected to each other through hierarchical and peer relationships, a computer system where computer hardware and software are connected to each other through various kinds of links, and a knowledge system where ideas and what can be done with the ideas are linked together.
The general convention of “node(s)” and “arc(s)” has been adapted herein to generally cover all network components and interconnections. The topologies of networks are important because similar topologies are expected to share generic properties and behaviour in a well-defined context. One may view the notion of topology in a way similar to human notions of shape (the object does not have sharp corners or the object is roughly a sphere or the object looks like a box, etc.). Topologies describe which kinds of nodes are connected to which other kinds of nodes.
A difficulty that often arises is deciding whether two networks are equivalent. This is especially problematic when each network uses a different set of names for its nodes. Two networks are said to be identical if each node of one can be placed upon an unoccupied node of the other in such a manner that the arcs (connectivities) of the two networks match. On the other hand, determining the topological equivalence or otherwise between two networks, using a representation having nodes interconnected by arcs, is comparatively simpler because the nomenclature is shared between the networks.